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Tikhonov Regularization for Functional Minimum Distance Estimators

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Author Info

  • P. Gagliardini

    (University of Lugano and Swiss Finance Institute)

  • O. Scaillet

    (University of Geneva and Swiss Finance Institute)

Abstract

We study the asymptotic properties of a Tikhonov Regularized (TiR) estimator of a functional parameter based on a minimum distance principle for nonparametric conditional moment restrictions. The estimator is computationally tractable and takes a closed form in the linear case. We derive its asymptotic Mean Integrated Squared Error (MISE), its rate of convergence and its pointwise asymptotic normality under a regularization parameter depending on sample size. The optimal value of the regularization parameter is characterized. We illustrate our theoretical findings and the small sample properties with simulation results for two numerical examples. We also discuss two data driven selection procedures of the regularization parameter via a spectral representation and a subsampling approximation of the MISE. Finally, we provide an empirical application to nonparametric estimation of an Engel curve.

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Bibliographic Info

Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 06-30.

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Length: 67 pages
Date of creation: May 2006
Date of revision: Nov 2006
Handle: RePEc:chf:rpseri:rp0630

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Web page: http://www.SwissFinanceInstitute.ch
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Related research

Keywords: MinimumDistance; Nonparametric Estimation; III-posed In-verse Problems; Tikhonov Regularization; Endogeneity; InstrumentalVariable; Generalized Method of Moments; Subsampling; Engelcurve.;

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Cited by:
  1. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
  2. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
  3. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.

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